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A & B are partners sharing profits and losses in the ratio 5:3. On admission C brings Rs. 70,000 cash and Rs. 48,000 against goodwill. New profit sharing ratio between A, B and C are 7:5:4. Find the sacrificing ratio as A:B
  • a)
    3:1.
  • b)
    4:7.
  • c)
    5:4.
  • d)
    2:1.
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
A B are partners sharing profits and losses in the ratio 5:3. On admi...
Given:
- A and B are partners sharing profits and losses in the ratio 5:3.
- C brings Rs. 70,000 cash and Rs. 48,000 against goodwill.
- The new profit sharing ratio between A, B, and C is 7:5:4.
To find:
The sacrificing ratio as A:B.

1. The partnership ratio of A and B before C's admission is 5:3.
2. Let's calculate the initial capitals of A and B:
- Let the initial capital of A be 5x.
- Let the initial capital of B be 3x.
3. The total initial capital is 5x + 3x = 8x.
4. C brings Rs. 70,000 in cash, so the new capital of C is 70,000.
5. C also brings Rs. 48,000 against goodwill, which will be added to the total capital.
- So, the new total capital is 70,000 + 48,000 = 118,000.
6. The new profit sharing ratio is 7:5:4, which can be written as 7x:5x:4x.
7. The difference in the capitals of A and B is the sacrificing ratio.
- Sacrificing ratio = (Initial capital of A - New capital of A):(Initial capital of B - New capital of B)
- Sacrificing ratio = (5x - 7x):(3x - 5x)
- Sacrificing ratio = -2x : -2x
- Simplifying, we get the sacrificing ratio as 2:1.
Final Answer:
The sacrificing ratio as A:B is 2:1.
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A B are partners sharing profits and losses in the ratio 5:3. On admi...
Understanding the Profit Sharing Ratio
- Initial Ratio: A and B share profits in the ratio of 5:3.
- New Ratio: After the admission of C, the new profit sharing ratio among A, B, and C is 7:5:4.
Calculating Sacrificing Ratio
To find the sacrificing ratio, we need to determine how much A and B have sacrificed in their original profit share to accommodate C.
- Total Parts in New Ratio: 7 + 5 + 4 = 16 parts.
- A's New Share: 7/16
- B's New Share: 5/16
- C's Share: 4/16
Calculating Old Shares
- A's Old Share: 5/8 (since 5 + 3 = 8)
- B's Old Share: 3/8
Calculating Sacrificing Amounts
- A's Sacrifice:
- Old Share: 5/8 = 10/16
- New Share: 7/16
- Sacrifice: 10/16 - 7/16 = 3/16
- B's Sacrifice:
- Old Share: 3/8 = 6/16
- New Share: 5/16
- Sacrifice: 6/16 - 5/16 = 1/16
Determining the Sacrificing Ratio
Now, we can express the sacrificing amounts of A and B in their simplest form:
- A's Sacrifice: 3/16
- B's Sacrifice: 1/16
Thus, the sacrificing ratio of A to B is:
- A:B = 3:1
Conclusion
The correct answer is option 'A' (3:1), indicating that A sacrifices more of their profit share compared to B to accommodate C in the partnership.
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A B are partners sharing profits and losses in the ratio 5:3. On admission C brings Rs. 70,000 cash and Rs. 48,000 against goodwill. New profit sharing ratio between A, B and C are 7:5:4. Find the sacrificing ratio as A:Ba)3:1.b)4:7.c)5:4.d)2:1.Correct answer is option 'A'. Can you explain this answer?
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